Battery dc impedance measurement

ABSTRACT

The state of charge of a rechargeable battery is determined by calculating the DC impedance of the battery. The impedance is calculated by: performing a two different constant current discharges of the battery at a first and second C-rates, respectively; measuring the voltage and current during the interval of each constant current discharge and calculating the amount of charge extracted from the battery up to a point where the battery voltage drops to a threshold value; calculating the state of charge of the battery; and calculating the DC impedance of the battery as a function of the difference between the battery voltages and discharge currents for the two different discharges.

PRIORITY CLAIM

This application claims priority from European Application for PatentNo. 13368021.5 filed Jul. 16, 2013, the disclosure of which isincorporated by reference.

TECHNICAL FIELD

This invention is relevant to methods for measuring the remainingcapacity of a rechargeable battery.

BACKGROUND

Many portable electronic devices nowadays comprise rechargeablebatteries, and it is useful, if not imperative, that a user of such adevice can readily gauge the amount of power remaining in the battery.Knowing the instantaneous remaining battery capacity helps the user toestimate how long the device can be used, for a given duty cycle, beforeits battery needs to be recharged.

As such, most battery-powered devices are provided with a “fuel gauge”type indicator, which is commonly in the form of “bars” of a graphicaluser interface (GUI) element, or a series of LED indicators. Bydisplaying the remaining battery charge, the user can judge whether, andhow, to continue using the device.

Existing battery charge level indicators comprise circuitry thatinterfaces with, and which measures certain parameters of the battery,and a computational element that converts the measurements into a usefulindication of the remaining battery power.

The two most commonly used display formats are obtained via a State ofCharge (SoC) calculation, which yields either a percentage remainingbattery charge, and/or the remaining battery capacity, say, in mAh. Inaddition, it is also possible to measure the instantaneous, or average,power consumption of the device to yield a “time to fully-discharged”indication in units of time. Most portable electronic devices areconfigured to operate differently depending on the battery charge level.In essence, functionality can be reduced as the remaining battery powerdrops below certain thresholds, such that the device can befully-operational (i.e. all features operative) above a first certainthreshold level, with functionality being withdrawn as the batterycharge level decreases. For example, the screen brightness may bedimmed, WiFi disabled, power-hungry applications disabled, etc. toconserver power as the remaining battery power drops below a series ofpre-defined threshold values.

Commonly, therefore, the SoC indicator provides a “100%” reading whenthe battery is fully charged, and a “0%” reading when the battery chargelevel drops below a voltage cut-off threshold value. Usefully, thevoltage cut-off threshold value does not correspond to 0% remainingbattery power, to enable certain device functionality, such as a RAMmaintenance voltage, an internal clock, the charging control circuitry,and so on, to persist even when the device notionally switched-off. Sucha configuration enables the device to operate correctly when it isconnected to a charging power source, even though its functionality maybe pared-down until the battery charge level exceeds the voltage cut-offthreshold value.

The voltage cut-off threshold value depends on the device manufacturer'spreferences, although this voltage is usually around 3.2V to 3.0V.

The remaining battery power calculation is typically performed via: avoltage approach, whereby the battery voltage is measured and comparedwith a value stored in a lookup table of voltages versus internalbattery impedances—the intersection yielding a State of Charge or theremaining capacity. Additionally or alternatively, a “coulomb counter”approach can be used, whereby the remaining capacity calculation isbased on measuring the current flowing into, and out of, the batterythrough a sense resistor. Summing of the “in” and “out” currents cangive the total charge that has flown from (e.g. by use), or to (e.g. viacharging), the battery and the capacity can be then calculated.

The above two techniques are often used both together in proprietaryalgorithms to provide the best accuracy.

To obtain a SoC estimation using the above “voltage” approach, themeasured battery voltage must be corrected by a voltage drop factor as aresult of the battery's internal impedance. The known way to measure theinternal impedance of the battery is the so-called “relaxation method”as described in, for example, “Battery management systems—AccurateState-of-charge indication for battery-powered applications”, V. Pop andal., Philips Research Book Series, Volume 9, Springer Science—2010 (thedisclosure of which is incorporated by reference). This techniqueinvolves discharging the battery followed by a rest period, whereby theimpedance is calculated by the voltage difference divided by the currentload, as set forth in equation 1 below:

Z _(int)=(V _(rest) −V _(min))/I _(Load)   (Eq. 1)

Where

-   -   Z_(int) is the internal battery impedance    -   V_(rest) is the battery voltage after a rest    -   V_(min) is the battery voltage loaded by the current I_(Load)    -   I_(load) is the current load applied to discharge the battery        for a while (discharge pulse time depends on the number of        points to characterize the battery impedance)

The main problem with the known SoC estimation techniques lies in thatthe characterization of the impedance of the battery must be performedusing specialized laboratory equipment. Because the battery ischaracterized under laboratory conditions, the characterization mightnot transpose correctly in actual use, for example when run in an actualapplication environment. Also, because the battery characterization iscarried out independently of system design, the PCB of the hardwareand/or the application cannot be taken into account at duringcharacterization, which can lead to inaccuracy in use.

A better approach would be to obtain an impedance reading directly inthe application layer, or by the system/device, in use, using real timemeasurement tools available on the system.

Another drawback of laboratory-based battery characterization subsistsin the time it takes to perform the characterization, which can be verylong. As described above, the DC impedance can be easily estimated bythe by the relaxation method, but this method requires a discharge and arest time of about 1 hour to be sure that the battery is really in therelaxed phase after stress due to the current load. Therefore, if 100data points are required, per battery, for the SoC algorithm to workproperly, it will take at least 100 hours of characterization time andso the characterization of a battery usually takes around 5 full days tocomplete.

A need therefore exists for an improved and/or an alternative way toobtain the DC impedance of a rechargeable battery without necessarilyhaving to resort to expensive, and time-consuming, laboratory-basedcharacterization techniques. More specifically, a need exists for amethod and/or an apparatus that can obtain the state of charge of arechargeable battery using battery impedance measurements taken usingon-system components.

SUMMARY

In an embodiment, a method of determining state of charge of arechargeable battery comprises: calculating the DC impedance of thebattery by: performing a first constant current discharge of the batteryat a first C-rate; measuring the voltage and current during the intervalof the first constant current discharge and calculating the amount ofcharge extracted from the battery up to a point i, whereby the batteryvoltage drops to a threshold value; calculating the state of charge asbeing equal to ((Q_(max)−Q_(i))/Q_(max))×100, where Q_(max) is the totalcharge extracted from the battery, and where Q_(i) is the amount ofcharge extracted at the point i, performing a second constant currentdischarge of the battery at a second C-rate lower than the first C-rate;measuring the voltage and current during the interval of the secondconstant current discharge and calculating the amount of chargeextracted from the battery up to a point i, whereby the battery voltagedrops to a threshold value; calculating the state of charge as beingequal to ((Q_(max)−Q_(i))/Q_(max))×100, where Q_(max) is the totalcharge extracted from the battery, and where Q_(i) is the amount ofcharge extracted at the point i, and calculating the DC impedance of thebattery, for a given state of charge as being:(Vbat_(second C-rate)−Vbat_(first C-rate))/(Iload_(first C-rate)−Iload_(second C-rate)),where Vbat_(second c-rate) and Vbat_(first c-rate) are the batteryvoltages measured at the second C-rate and the first C-rate,respectively and where Iload_(second C-rate) and Iload_(first C-rate)are the current load when discharging at the second C-rate and the firstC-rate, respectively.

Suitably, the amount of charge extracted from the battery can becalculated by recording the current load at intervals through thedischarge and by multiplying the current at each interval by theduration of the respective interval. The total charge extracted can becalculated by summing the charge extracted during each interval.

The threshold value is suitably a battery voltage of substantially 3.0V.

The temperature of the battery is suitably measured, and logged, duringthe first and second constant discharges.

The C-rate is suitably a current used to charge/discharge the batteryand may be a part of the nominal capacity current of the battery perhour. For example, a 1000 mAh charge/discharge at 0.8C rate is chargedwith a current of 800 mA. In other words, the C-rate is a measure of therate of charging or discharging the battery expressed as thecharge/discharge current divided by the nominal capacity rating of thebattery.

The DC impedance of the battery can be obtained relatively easilybecause it is only necessary to perform two constant current dischargesat different C-rates, nominally, a low C-rate and a high C-rate, such as0.1C and 0.3C; or 0.2C and 0.7C, for example.

During the constant current discharges, it is preferable that theambient temperature is in the range of approximately 23-25° C., whichmay ensure consistency between measurements, and to yield a result thatis representative of “normal use”. However, the measurements could beperformed at different temperatures, and a temperature correctionfactored in when calculating the impedance of the battery subsequently.

The impedance of the battery is suitably calculated for different SoCvalues, depending on the number of data points that are required by theSoC calculation software. However, because the method yields a series ofDC impedances, i.e. by recording the voltage and current at intervalsdetermined by the user (e.g. at 1-second, or 10-second intervals), thenumber of impedance values obtained is directly linked to the number ofpoint used during the constant current discharges. As such, theinvention yields a large number impedance values in a much shorter timethan if a “relaxation” test were to be performed for each data point.

It has been found, experimentally, that a two-discharge impedancecalculation is approximately as accurate as the impedance valuesobtained by a series of “relaxation” tests. However, it will beappreciated that the accuracy of the impedance measurements couldpotentially be increased by performing more than two constant currentdischarges, and by comparing the results across more than one pair ofvalues. For example, by performing three discharges, there would be twopairs of values to compare, or if four dischargers were performed, thenthere would be six pairs of values to compare, and so on.

A temperature correction algorithm can suitably be used to obtain theimpedance under other battery temperature measurement conditions.Suitably, the method also provides the option of obtaining theopen-circuit voltage of the battery by using the low C-rate voltage (orhigh C-rate voltage) and adding the voltage drop due to the internalbattery impedance (that has just been calculated). So, the open circuitvoltage is given by: V_(OCV)(SoC,T)=V_(Bat)(SOC,T)+Z_(int)(SOC,T)×I_(load).

BRIEF DESCRIPTION OF THE DRAWINGS

A preferred embodiment of the invention shall now be described, by wayof example only, with reference to the accompanying drawings in which:

FIG. 1 is a schematic showing a system;

FIG. 2 is a schematic graph of current versus time during a constantcurrent charge test; and

FIG. 3 is a schematic graph of voltage and current as a function of SoCfor two C-rates.

DETAILED DESCRIPTION OF THE DRAWINGS

In FIG. 1, a rechargeable battery 10 is discharged through a constantcurrent load 12. During the discharge, the battery voltage is measuredby a voltmeter 14 and the discharge current is measured by an ammeter16. The battery 10 comprises a temperature sensor 18, and the system 20comprises an internal clock 22.

A first C-rate is selected, and the discharge test begins. At intervalsdetermined by the user (or application), and timed by the system clock22, voltage, current and temperature readings are taken by the voltmeter14, ammeter 16 and temperature sensor 18, respectively. These values arerecorded in a log 24 comprising a table of time 26, temperature 28,voltage 30 and current 32. The discharge continues until the voltage 30reaches a threshold cut-off value, typically 3.0V.

The log 24 is then interrogated, and the charge extracted from thebattery 10 is calculated, as shown in FIG. 2. Here, the current 32 isplotted as a function of time 26, and the charge is simply the areaunder the curve 34. The total current extracted can be calculated bysumming the area under the curve 34 (Q1+Q2+Q3+Qn).

Next, the voltage 30 and current 32 is plotted as a function of SoC, asshown in FIG. 3.

The test is then repeated at a second C-rate, following the steps above,and the voltage 30 and current 32 values plotted in the graph of FIG. 3.

Now, for a given SoC value, it is possible to read off a correspondingvoltage and current for each of the C-rate discharges, as shown in FIG.3, whereby the values of V_(high C-rate) 40, V_(low C-rate) 42,i_(high C-rate) 44 and i_(low C-rate) 46 can be seen. These values canthen be fed into the equation:

Z _(int) (SoC, T)=(Vbat_(low C-rate)−Vbat_(high C-rate))/(Iload_(high C-rate) −Iload_(low C-rate))   (Eq. 3)

to obtain the impedance of the battery 10 at that particular SoC value.The calculation can be repeated for different SoC values, and of course,for different temperatures.

The resultant impedance values can be stored for later use by a SoCalgorithm to correct for variations in the battery 10 impedance atdifferent temperatures, voltages and SoC levels.

Advantageously, the invention may provide a relatively easy way toobtain the impedance of the battery without having to perform detailedand time-consuming impedance characterization tests (e.g. relaxationtests). Experiments have shown that the calculated impedances, obtainedby the invention, are reasonably accurate, and that the impedancecalculations can be performed on-system, thereby yielding a morerealistic “actual use” values, that could, say, a laboratory-basedcharacterization methodology. In addition, the invention may enablesystem designers or end users to perform impedance characterization forparticular batteries, making it possible to characterize multiplebatteries for a single application. Owing to the greater granularity ofthe invention, a greater number of data points can be obtained, comparedto the individual relaxation tests, thereby potentially increasing theaccuracy of the characterization process whilst also reducing the costand time of characterization.

What is claimed is:
 1. A method of determining the state of charge of arechargeable battery comprising the steps of: calculating the DCimpedance of the battery by: performing a first constant currentdischarge of the battery at a first C-rate; measuring the voltage andcurrent during the interval of the first constant current discharge andcalculating the amount of charge extracted from the battery up to apoint i, whereby the battery voltage drops to a threshold value;calculating the state of charge as being equal to(((Q_(max)−Q_(i)))/Q_(max))×100, where Q_(max) is the total chargeextracted from the battery, and where Q_(i) is the amount of chargeextracted at the point i; performing a second constant current dischargeof the battery at a second C-rate lower than the first C-rate; measuringthe voltage and current during the interval of the second constantcurrent discharge and calculating the amount of charge extracted fromthe battery up to the point i, whereby the battery voltage drops to athreshold value; calculating the state of charge as being equal to((Q_(max)−Q_(i)))/Q_(max))×100, where Q_(max) is the total chargeextracted from the battery, and where Q_(i) is the amount of chargeextracted at the point i; and calculating the DC impedance of thebattery, for a given state of charge as being:((Vbat_(second C-rate)−Vbat_(first C-rate))/(Iload_(first C-rate)−Iload_(second C-rate)),where Vbat_(second C-rate) and Vbat_(first C-rate) are the batteryvoltages measured at the second C-rate and the first Crate,respectively, and where Iload_(second C-rate) and Iload_(first C-rate)are the current load when discharging at the second C-rate and the firstC-rate, respectively.
 2. The method of claim 1, wherein the amount ofcharge extracted from the battery is calculated by recording the currentload at intervals throughout the discharge and by multiplying thecurrent at each interval by the duration of each respective interval. 3.The method of claim 2, further comprising the step of recording in a logthe measured currents and times when the currents are measured, andinterrogating the log to calculate the charge extracted from the batteryduring the interval between a pair of times, by multiplying the intervalby the average of the corresponding current measurements.
 4. The methodof claim 2, wherein the total charge extracted is calculated by summingthe charges extracted during each interval.
 5. The method of claim 1,wherein the threshold value comprises a battery voltage of substantially3.0V.
 6. The method of claim 1, further comprising the step of measuringand logging the battery temperature during the first and second constantdischarges.
 7. The method of claim 1, wherein the first C-rate is 0.8C,0.7C or 0.3C, and wherein the second C-rate is 0.1C or 0.2C.
 8. Themethod of claim 1, wherein the constant current discharges are performedat substantially the same ambient temperature.
 9. The method of claim 8,wherein the ambient temperature is in the range of approximately 23-25°C.
 10. The method of claim 1, performed using more than two constantcurrent discharges, and by comparing the results across more than onepair of values.
 11. The method of claim 1, further comprising the stepof providing a log of the measured currents, voltages, temperatures andtimes for each C-rate discharge, plotting the voltage and current as afunction of SoC for each C-rate discharge, determining a voltage andcurrent for a specified SoC for each of the C-rate discharges, wherebythe values of V_(high C-rate), V_(low C-rate), i_(high C-rate) andi_(low C-rate) are used to obtain the battery impedance at the specifiedSoC according to the equation:Z _(int) (SoC,T)=(Vbat_(low C-rate)−Vbat_(high C-rate))/(Iload_(high C-rate) −Iload_(low C-rate)).
 12. Themethod of claim 11, wherein the calculation is repeated for differentSoC values.
 13. The method of claim 11, therein the calculation isrepeated at different temperatures.
 14. The method of claim 11, whereinthe resultant calculated battery impedance values are stored for lateruse by a SoC algorithm for correct for variations in the batteryimpedance at different temperatures, voltages and SoC levels.
 15. Themethod of claim 1, further comprising the step of determining theopen-circuit voltage VOCV (SoC,T) of the battery using the low C-ratevoltage and adding the voltage drop due to the calculated internalbattery impedance according to:V _(OCV) (SoC,T)=V _(Bat) (SoC,T)+Z _(int) (SoC,T)×I _(load).
 16. Anapparatus, comprising: a circuit configured to determine the state ofcharge of a rechargeable battery comprising: a discharge circuitconfigured to discharge the rechargeable battery through a constantcurrent load, a voltmeter configured to measure the rechargeable batteryvoltage, an ammeter configured to measure the discharge current, atemperature sensor configured to measure temperature, a processorcomprising an internal clock and configured to select a desired C-ratefor discharging the battery through the load, monitor and log thevoltage, current and temperature at intervals determined by the clock,and determine the state of charge of the rechargeable battery accordingto the method of claim
 1. 17. The apparatus of claim 16, furthercomprising a disconnect circuit configured to disconnect the batteryfrom the load when the voltage reaches a threshold cut-off value. 18.The apparatus of claim 16, further comprising a memory for storing a logof any one or more of the measured voltages, currents, temperatures andtimes when the currents, voltages and temperatures are measured.